Abstract This paper deals with inverse displacement analysis of a Hyper-redundant Elephant’s Trunk Robot (HRETR). The HRETR is con-nected in series with n modules of 3UPS-PRU parallel mechanism where the underline P denotes an active prismatic joint. Based on the idea of differential geometry, backbone curve of the robot is formulated by using a parametric function consisting of sub-functions and control parameters. A general algorithm for generating a backbone curve and fitting the modules to the backbone curve is proposed. In this way, the inverse displacement analysis of the robot can be carried out by solving the inverse displacement problem of each parallel mechanism module and taking into account the length limits of the links. A HRETR with 6 modules is taken as an example to demonstrate the applicability of the algorithm.